A device of this type is disclosed in EP-A-800 163. In this device, an average value is formed from the scanning signal and serves as input signal of the data slicer. A control unit serves to change the time constant for the averaging process when a great change occurs in the analogue scanning signal, caused by boundaries of different areas of data tracks on the recording medium. The known device may be regarded as having the disadvantage that although an adaptation of the average value in the case of a transition from one type of data area to another takes place more rapidly than without a change in the time constant, an adaptation of the average value is nonetheless restricted to this type of transition.